Asymptotically exact/conservative confidence bands are obtained for nonparametric regression function, based on piecewise constant/linear polynomial spline estimation, respectively. Compared to the pointwisenonparametric confidence interval of Huang (2003), the confidence bands are inflated only by a factor of square root of logarithm of sample size, similar to the Nadaraya-Watson confidence band of H\"{a}rdle (1989), and the local polynomial bands of Xia (1998) and Claeskens and Van Keilegom (2003). Simulation experiments have provided strong evidence that corroborates with the asymptotic theory. Testing against the linear spline confidence band, the commonly used trigonometric trend is rejected with highly significant evidence for the Leaf Area Index of Aquatic Agriculture land, based on the remote sensing data collected from East Africa.
Joint work with Ph.D. student Jing Wang, partially supported by NSF grants DMS 0405330, BCS 0308420, SES 0127722.

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